find \\( \\frac{d p}{d q} \\) for \\( p=\\frac{\\cos q+\\sin q}{\\cos q} \\).\n\\( \\frac{d p}{d q}=\\square…

find \\( \\frac{d p}{d q} \\) for \\( p=\\frac{\\cos q+\\sin q}{\\cos q} \\).\n\\( \\frac{d p}{d q}=\\square \\)

find \\( \\frac{d p}{d q} \\) for \\( p=\\frac{\\cos q+\\sin q}{\\cos q} \\).\n\\( \\frac{d p}{d q}=\\square \\)

Answer

Explanation:

Step1: Simplify the function

First, simplify ( p=\frac{\cos q+\sin q}{\cos q}=1 + \tan q) (since (\frac{\sin q}{\cos q}=\tan q)).

Step2: Differentiate using basic rules

Differentiate (p = 1+\tan q) with respect to (q). The derivative of a constant (1) is (0), and the derivative of (\tan q) with respect to (q) is (\sec^{2}q) (using the formula (\frac{d}{dq}(\tan q)=\sec^{2}q)).

Answer:

(\sec^{2}q)